Cubic critical

Percentage Accurate: 52.1% → 84.9%

Time: 14.2s

Alternatives: 12

Speedup: 16.4×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Initial Program: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+82}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-24}:\\ \;\;\;\;\frac{\sqrt{b \cdot b - \left(a \cdot 3\right) \cdot c} - b}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -4e+82)
   (/ (/ (* b 2.0) a) -3.0)
   (if (<= b 4e-24)
     (/ (- (sqrt (- (* b b) (* (* a 3.0) c))) b) (* a 3.0))
     (/ (* c -0.5) b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -4e+82) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 4e-24) {
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4d+82)) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else if (b <= 4d-24) then
        tmp = (sqrt(((b * b) - ((a * 3.0d0) * c))) - b) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -4e+82) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 4e-24) {
		tmp = (Math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -4e+82:
		tmp = ((b * 2.0) / a) / -3.0
	elif b <= 4e-24:
		tmp = (math.sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -4e+82)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	elseif (b <= 4e-24)
		tmp = Float64(Float64(sqrt(Float64(Float64(b * b) - Float64(Float64(a * 3.0) * c))) - b) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -4e+82)
		tmp = ((b * 2.0) / a) / -3.0;
	elseif (b <= 4e-24)
		tmp = (sqrt(((b * b) - ((a * 3.0) * c))) - b) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -4e+82], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[b, 4e-24], N[(N[(N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(a * 3.0), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.3333333333333333 \cdot \frac{b + \sqrt{a \cdot \left(-3 \cdot c\right)}}{a}\\ \mathbf{if}\;b \leq -5.4 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (* 0.3333333333333333 (/ (+ b (sqrt (* a (* -3.0 c)))) a))))
   (if (<= b -5.4e-50)
     (/ (/ (* b 2.0) a) -3.0)
     (if (<= b 3.2e-67)
       t_0
       (if (<= b 2.9e-31)
         (* -0.5 (/ c b))
         (if (<= b 1.15e-24) t_0 (/ (* c -0.5) b)))))))

C

double code(double a, double b, double c) {
	double t_0 = 0.3333333333333333 * ((b + sqrt((a * (-3.0 * c)))) / a);
	double tmp;
	if (b <= -5.4e-50) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 3.2e-67) {
		tmp = t_0;
	} else if (b <= 2.9e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 1.15e-24) {
		tmp = t_0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.3333333333333333d0 * ((b + sqrt((a * ((-3.0d0) * c)))) / a)
    if (b <= (-5.4d-50)) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else if (b <= 3.2d-67) then
        tmp = t_0
    else if (b <= 2.9d-31) then
        tmp = (-0.5d0) * (c / b)
    else if (b <= 1.15d-24) then
        tmp = t_0
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = 0.3333333333333333 * ((b + Math.sqrt((a * (-3.0 * c)))) / a);
	double tmp;
	if (b <= -5.4e-50) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 3.2e-67) {
		tmp = t_0;
	} else if (b <= 2.9e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 1.15e-24) {
		tmp = t_0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = 0.3333333333333333 * ((b + math.sqrt((a * (-3.0 * c)))) / a)
	tmp = 0
	if b <= -5.4e-50:
		tmp = ((b * 2.0) / a) / -3.0
	elif b <= 3.2e-67:
		tmp = t_0
	elif b <= 2.9e-31:
		tmp = -0.5 * (c / b)
	elif b <= 1.15e-24:
		tmp = t_0
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	t_0 = Float64(0.3333333333333333 * Float64(Float64(b + sqrt(Float64(a * Float64(-3.0 * c)))) / a))
	tmp = 0.0
	if (b <= -5.4e-50)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	elseif (b <= 3.2e-67)
		tmp = t_0;
	elseif (b <= 2.9e-31)
		tmp = Float64(-0.5 * Float64(c / b));
	elseif (b <= 1.15e-24)
		tmp = t_0;
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = 0.3333333333333333 * ((b + sqrt((a * (-3.0 * c)))) / a);
	tmp = 0.0;
	if (b <= -5.4e-50)
		tmp = ((b * 2.0) / a) / -3.0;
	elseif (b <= 3.2e-67)
		tmp = t_0;
	elseif (b <= 2.9e-31)
		tmp = -0.5 * (c / b);
	elseif (b <= 1.15e-24)
		tmp = t_0;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(0.3333333333333333 * N[(N[(b + N[Sqrt[N[(a * N[(-3.0 * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.4e-50], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[b, 3.2e-67], t$95$0, If[LessEqual[b, 2.9e-31], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e-24], t$95$0, N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{-67}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{b + \sqrt{a \cdot \left(-3 \cdot c\right)}}{a}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{b + \sqrt{c \cdot \left(a \cdot -3\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -3.8e-49)
   (/ (/ (* b 2.0) a) -3.0)
   (if (<= b 2.85e-67)
     (* 0.3333333333333333 (/ (+ b (sqrt (* a (* -3.0 c)))) a))
     (if (<= b 2.6e-31)
       (* -0.5 (/ c b))
       (if (<= b 3.6e-25)
         (* 0.3333333333333333 (/ (+ b (sqrt (* c (* a -3.0)))) a))
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e-49) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 2.85e-67) {
		tmp = 0.3333333333333333 * ((b + sqrt((a * (-3.0 * c)))) / a);
	} else if (b <= 2.6e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 3.6e-25) {
		tmp = 0.3333333333333333 * ((b + sqrt((c * (a * -3.0)))) / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-3.8d-49)) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else if (b <= 2.85d-67) then
        tmp = 0.3333333333333333d0 * ((b + sqrt((a * ((-3.0d0) * c)))) / a)
    else if (b <= 2.6d-31) then
        tmp = (-0.5d0) * (c / b)
    else if (b <= 3.6d-25) then
        tmp = 0.3333333333333333d0 * ((b + sqrt((c * (a * (-3.0d0))))) / a)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -3.8e-49) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 2.85e-67) {
		tmp = 0.3333333333333333 * ((b + Math.sqrt((a * (-3.0 * c)))) / a);
	} else if (b <= 2.6e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 3.6e-25) {
		tmp = 0.3333333333333333 * ((b + Math.sqrt((c * (a * -3.0)))) / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -3.8e-49:
		tmp = ((b * 2.0) / a) / -3.0
	elif b <= 2.85e-67:
		tmp = 0.3333333333333333 * ((b + math.sqrt((a * (-3.0 * c)))) / a)
	elif b <= 2.6e-31:
		tmp = -0.5 * (c / b)
	elif b <= 3.6e-25:
		tmp = 0.3333333333333333 * ((b + math.sqrt((c * (a * -3.0)))) / a)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -3.8e-49)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	elseif (b <= 2.85e-67)
		tmp = Float64(0.3333333333333333 * Float64(Float64(b + sqrt(Float64(a * Float64(-3.0 * c)))) / a));
	elseif (b <= 2.6e-31)
		tmp = Float64(-0.5 * Float64(c / b));
	elseif (b <= 3.6e-25)
		tmp = Float64(0.3333333333333333 * Float64(Float64(b + sqrt(Float64(c * Float64(a * -3.0)))) / a));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -3.8e-49)
		tmp = ((b * 2.0) / a) / -3.0;
	elseif (b <= 2.85e-67)
		tmp = 0.3333333333333333 * ((b + sqrt((a * (-3.0 * c)))) / a);
	elseif (b <= 2.6e-31)
		tmp = -0.5 * (c / b);
	elseif (b <= 3.6e-25)
		tmp = 0.3333333333333333 * ((b + sqrt((c * (a * -3.0)))) / a);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -3.8e-49], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[b, 2.85e-67], N[(0.3333333333333333 * N[(N[(b + N[Sqrt[N[(a * N[(-3.0 * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-31], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-25], N[(0.3333333333333333 * N[(N[(b + N[Sqrt[N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 79.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{b + \sqrt{a \cdot \left(-3 \cdot c\right)}}{a \cdot 3}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-31}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-24}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{b + \sqrt{c \cdot \left(a \cdot -3\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -5e-43)
   (/ (/ (* b 2.0) a) -3.0)
   (if (<= b 3.2e-67)
     (/ (+ b (sqrt (* a (* -3.0 c)))) (* a 3.0))
     (if (<= b 2.2e-31)
       (* -0.5 (/ c b))
       (if (<= b 6.2e-24)
         (* 0.3333333333333333 (/ (+ b (sqrt (* c (* a -3.0)))) a))
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-43) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 3.2e-67) {
		tmp = (b + sqrt((a * (-3.0 * c)))) / (a * 3.0);
	} else if (b <= 2.2e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 6.2e-24) {
		tmp = 0.3333333333333333 * ((b + sqrt((c * (a * -3.0)))) / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5d-43)) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else if (b <= 3.2d-67) then
        tmp = (b + sqrt((a * ((-3.0d0) * c)))) / (a * 3.0d0)
    else if (b <= 2.2d-31) then
        tmp = (-0.5d0) * (c / b)
    else if (b <= 6.2d-24) then
        tmp = 0.3333333333333333d0 * ((b + sqrt((c * (a * (-3.0d0))))) / a)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -5e-43) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 3.2e-67) {
		tmp = (b + Math.sqrt((a * (-3.0 * c)))) / (a * 3.0);
	} else if (b <= 2.2e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 6.2e-24) {
		tmp = 0.3333333333333333 * ((b + Math.sqrt((c * (a * -3.0)))) / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -5e-43:
		tmp = ((b * 2.0) / a) / -3.0
	elif b <= 3.2e-67:
		tmp = (b + math.sqrt((a * (-3.0 * c)))) / (a * 3.0)
	elif b <= 2.2e-31:
		tmp = -0.5 * (c / b)
	elif b <= 6.2e-24:
		tmp = 0.3333333333333333 * ((b + math.sqrt((c * (a * -3.0)))) / a)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -5e-43)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	elseif (b <= 3.2e-67)
		tmp = Float64(Float64(b + sqrt(Float64(a * Float64(-3.0 * c)))) / Float64(a * 3.0));
	elseif (b <= 2.2e-31)
		tmp = Float64(-0.5 * Float64(c / b));
	elseif (b <= 6.2e-24)
		tmp = Float64(0.3333333333333333 * Float64(Float64(b + sqrt(Float64(c * Float64(a * -3.0)))) / a));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -5e-43)
		tmp = ((b * 2.0) / a) / -3.0;
	elseif (b <= 3.2e-67)
		tmp = (b + sqrt((a * (-3.0 * c)))) / (a * 3.0);
	elseif (b <= 2.2e-31)
		tmp = -0.5 * (c / b);
	elseif (b <= 6.2e-24)
		tmp = 0.3333333333333333 * ((b + sqrt((c * (a * -3.0)))) / a);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -5e-43], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[b, 3.2e-67], N[(N[(b + N[Sqrt[N[(a * N[(-3.0 * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-31], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-24], N[(0.3333333333333333 * N[(N[(b + N[Sqrt[N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-67}:\\ \;\;\;\;\frac{\sqrt{a \cdot \left(-3 \cdot c\right)} - b}{a \cdot 3}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{b + \sqrt{c \cdot \left(a \cdot -3\right)}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b -8e-50)
   (/ (/ (* b 2.0) a) -3.0)
   (if (<= b 2.7e-67)
     (/ (- (sqrt (* a (* -3.0 c))) b) (* a 3.0))
     (if (<= b 3.1e-31)
       (* -0.5 (/ c b))
       (if (<= b 3.6e-25)
         (* 0.3333333333333333 (/ (+ b (sqrt (* c (* a -3.0)))) a))
         (/ (* c -0.5) b))))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= -8e-50) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 2.7e-67) {
		tmp = (sqrt((a * (-3.0 * c))) - b) / (a * 3.0);
	} else if (b <= 3.1e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 3.6e-25) {
		tmp = 0.3333333333333333 * ((b + sqrt((c * (a * -3.0)))) / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-8d-50)) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else if (b <= 2.7d-67) then
        tmp = (sqrt((a * ((-3.0d0) * c))) - b) / (a * 3.0d0)
    else if (b <= 3.1d-31) then
        tmp = (-0.5d0) * (c / b)
    else if (b <= 3.6d-25) then
        tmp = 0.3333333333333333d0 * ((b + sqrt((c * (a * (-3.0d0))))) / a)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= -8e-50) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 2.7e-67) {
		tmp = (Math.sqrt((a * (-3.0 * c))) - b) / (a * 3.0);
	} else if (b <= 3.1e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 3.6e-25) {
		tmp = 0.3333333333333333 * ((b + Math.sqrt((c * (a * -3.0)))) / a);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= -8e-50:
		tmp = ((b * 2.0) / a) / -3.0
	elif b <= 2.7e-67:
		tmp = (math.sqrt((a * (-3.0 * c))) - b) / (a * 3.0)
	elif b <= 3.1e-31:
		tmp = -0.5 * (c / b)
	elif b <= 3.6e-25:
		tmp = 0.3333333333333333 * ((b + math.sqrt((c * (a * -3.0)))) / a)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= -8e-50)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	elseif (b <= 2.7e-67)
		tmp = Float64(Float64(sqrt(Float64(a * Float64(-3.0 * c))) - b) / Float64(a * 3.0));
	elseif (b <= 3.1e-31)
		tmp = Float64(-0.5 * Float64(c / b));
	elseif (b <= 3.6e-25)
		tmp = Float64(0.3333333333333333 * Float64(Float64(b + sqrt(Float64(c * Float64(a * -3.0)))) / a));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= -8e-50)
		tmp = ((b * 2.0) / a) / -3.0;
	elseif (b <= 2.7e-67)
		tmp = (sqrt((a * (-3.0 * c))) - b) / (a * 3.0);
	elseif (b <= 3.1e-31)
		tmp = -0.5 * (c / b);
	elseif (b <= 3.6e-25)
		tmp = 0.3333333333333333 * ((b + sqrt((c * (a * -3.0)))) / a);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, -8e-50], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[b, 2.7e-67], N[(N[(N[Sqrt[N[(a * N[(-3.0 * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-31], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-25], N[(0.3333333333333333 * N[(N[(b + N[Sqrt[N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\sqrt{c \cdot \left(a \cdot -3\right)} - b}{a \cdot 3}\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{-67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-31}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (let* ((t_0 (/ (- (sqrt (* c (* a -3.0))) b) (* a 3.0))))
   (if (<= b -3.5e-45)
     (/ (/ (* b 2.0) a) -3.0)
     (if (<= b 2.85e-67)
       t_0
       (if (<= b 2.3e-31)
         (* -0.5 (/ c b))
         (if (<= b 3.8e-25) t_0 (/ (* c -0.5) b)))))))

C

double code(double a, double b, double c) {
	double t_0 = (sqrt((c * (a * -3.0))) - b) / (a * 3.0);
	double tmp;
	if (b <= -3.5e-45) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 2.85e-67) {
		tmp = t_0;
	} else if (b <= 2.3e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 3.8e-25) {
		tmp = t_0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (sqrt((c * (a * (-3.0d0)))) - b) / (a * 3.0d0)
    if (b <= (-3.5d-45)) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else if (b <= 2.85d-67) then
        tmp = t_0
    else if (b <= 2.3d-31) then
        tmp = (-0.5d0) * (c / b)
    else if (b <= 3.8d-25) then
        tmp = t_0
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double t_0 = (Math.sqrt((c * (a * -3.0))) - b) / (a * 3.0);
	double tmp;
	if (b <= -3.5e-45) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else if (b <= 2.85e-67) {
		tmp = t_0;
	} else if (b <= 2.3e-31) {
		tmp = -0.5 * (c / b);
	} else if (b <= 3.8e-25) {
		tmp = t_0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	t_0 = (math.sqrt((c * (a * -3.0))) - b) / (a * 3.0)
	tmp = 0
	if b <= -3.5e-45:
		tmp = ((b * 2.0) / a) / -3.0
	elif b <= 2.85e-67:
		tmp = t_0
	elif b <= 2.3e-31:
		tmp = -0.5 * (c / b)
	elif b <= 3.8e-25:
		tmp = t_0
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	t_0 = Float64(Float64(sqrt(Float64(c * Float64(a * -3.0))) - b) / Float64(a * 3.0))
	tmp = 0.0
	if (b <= -3.5e-45)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	elseif (b <= 2.85e-67)
		tmp = t_0;
	elseif (b <= 2.3e-31)
		tmp = Float64(-0.5 * Float64(c / b));
	elseif (b <= 3.8e-25)
		tmp = t_0;
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	t_0 = (sqrt((c * (a * -3.0))) - b) / (a * 3.0);
	tmp = 0.0;
	if (b <= -3.5e-45)
		tmp = ((b * 2.0) / a) / -3.0;
	elseif (b <= 2.85e-67)
		tmp = t_0;
	elseif (b <= 2.3e-31)
		tmp = -0.5 * (c / b);
	elseif (b <= 3.8e-25)
		tmp = t_0;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := Block[{t$95$0 = N[(N[(N[Sqrt[N[(c * N[(a * -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - b), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e-45], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], If[LessEqual[b, 2.85e-67], t$95$0, If[LessEqual[b, 2.3e-31], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.8e-25], t$95$0, N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 67.4% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;\frac{b \cdot -2}{a \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.6e-264) (/ (* b -2.0) (* a 3.0)) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = (b * -2.0) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 2.6d-264) then
        tmp = (b * (-2.0d0)) / (a * 3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = (b * -2.0) / (a * 3.0);
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.6e-264:
		tmp = (b * -2.0) / (a * 3.0)
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.6e-264)
		tmp = Float64(Float64(b * -2.0) / Float64(a * 3.0));
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 2.6e-264)
		tmp = (b * -2.0) / (a * 3.0);
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.6e-264], N[(N[(b * -2.0), $MachinePrecision] / N[(a * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 67.4% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;\frac{\frac{b \cdot 2}{a}}{-3}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.6e-264) (/ (/ (* b 2.0) a) -3.0) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 2.6d-264) then
        tmp = ((b * 2.0d0) / a) / (-3.0d0)
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = ((b * 2.0) / a) / -3.0;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.6e-264:
		tmp = ((b * 2.0) / a) / -3.0
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.6e-264)
		tmp = Float64(Float64(Float64(b * 2.0) / a) / -3.0);
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 2.6e-264)
		tmp = ((b * 2.0) / a) / -3.0;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.6e-264], N[(N[(N[(b * 2.0), $MachinePrecision] / a), $MachinePrecision] / -3.0), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 67.4% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;-0.6666666666666666 \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.6e-264) (* -0.6666666666666666 (/ b a)) (* -0.5 (/ c b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = -0.5 * (c / b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 2.6d-264) then
        tmp = (-0.6666666666666666d0) * (b / a)
    else
        tmp = (-0.5d0) * (c / b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = -0.6666666666666666 * (b / a);
	} else {
		tmp = -0.5 * (c / b);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.6e-264:
		tmp = -0.6666666666666666 * (b / a)
	else:
		tmp = -0.5 * (c / b)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.6e-264)
		tmp = Float64(-0.6666666666666666 * Float64(b / a));
	else
		tmp = Float64(-0.5 * Float64(c / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 2.6e-264)
		tmp = -0.6666666666666666 * (b / a);
	else
		tmp = -0.5 * (c / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.6e-264], N[(-0.6666666666666666 * N[(b / a), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 67.4% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;\frac{b \cdot -0.6666666666666666}{a}\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{c}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.6e-264) (/ (* b -0.6666666666666666) a) (* -0.5 (/ c b))))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = (b * -0.6666666666666666) / a;
	} else {
		tmp = -0.5 * (c / b);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 2.6d-264) then
        tmp = (b * (-0.6666666666666666d0)) / a
    else
        tmp = (-0.5d0) * (c / b)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = (b * -0.6666666666666666) / a;
	} else {
		tmp = -0.5 * (c / b);
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.6e-264:
		tmp = (b * -0.6666666666666666) / a
	else:
		tmp = -0.5 * (c / b)
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.6e-264)
		tmp = Float64(Float64(b * -0.6666666666666666) / a);
	else
		tmp = Float64(-0.5 * Float64(c / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 2.6e-264)
		tmp = (b * -0.6666666666666666) / a;
	else
		tmp = -0.5 * (c / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.6e-264], N[(N[(b * -0.6666666666666666), $MachinePrecision] / a), $MachinePrecision], N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 67.4% accurate, 16.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-264}:\\ \;\;\;\;\frac{b \cdot -0.6666666666666666}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{c \cdot -0.5}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (if (<= b 2.6e-264) (/ (* b -0.6666666666666666) a) (/ (* c -0.5) b)))

C

double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = (b * -0.6666666666666666) / a;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 2.6d-264) then
        tmp = (b * (-0.6666666666666666d0)) / a
    else
        tmp = (c * (-0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c) {
	double tmp;
	if (b <= 2.6e-264) {
		tmp = (b * -0.6666666666666666) / a;
	} else {
		tmp = (c * -0.5) / b;
	}
	return tmp;
}

Python

def code(a, b, c):
	tmp = 0
	if b <= 2.6e-264:
		tmp = (b * -0.6666666666666666) / a
	else:
		tmp = (c * -0.5) / b
	return tmp

Julia

function code(a, b, c)
	tmp = 0.0
	if (b <= 2.6e-264)
		tmp = Float64(Float64(b * -0.6666666666666666) / a);
	else
		tmp = Float64(Float64(c * -0.5) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c)
	tmp = 0.0;
	if (b <= 2.6e-264)
		tmp = (b * -0.6666666666666666) / a;
	else
		tmp = (c * -0.5) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_] := If[LessEqual[b, 2.6e-264], N[(N[(b * -0.6666666666666666), $MachinePrecision] / a), $MachinePrecision], N[(N[(c * -0.5), $MachinePrecision] / b), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 35.4% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ -0.5 \cdot \frac{c}{b} \end{array} \]

FPCore

(FPCore (a b c) :precision binary64 (* -0.5 (/ c b)))

C

double code(double a, double b, double c) {
	return -0.5 * (c / b);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-0.5d0) * (c / b)
end function

Java

public static double code(double a, double b, double c) {
	return -0.5 * (c / b);
}

Python

def code(a, b, c):
	return -0.5 * (c / b)

Julia

function code(a, b, c)
	return Float64(-0.5 * Float64(c / b))
end

MATLAB

function tmp = code(a, b, c)
	tmp = -0.5 * (c / b);
end

Wolfram

code[a_, b_, c_] := N[(-0.5 * N[(c / b), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023342 
(FPCore (a b c)
  :name "Cubic critical"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))